How to move an object without it completely teleporting somewhere else?
Judging by the video, it looks like you are constantly pressing the middle mouse button while moving the cylinder. Constantly pressing the middle mouse button and moving the mouse switches the axis and moves the object on that axis. This happens again and again which causes the teleportation effect.
You can fix this by:

Releasing the middle mouse button after selecting the required axis.
Instead of using middle mouse button, using X,Y,Z on keyboard to lock the axis.